Marginal Rate of Substitution
What is Marginal Rate of Substitution?
The marginal rate of substitution is the rate at which a consumer will give up one good to get more of another while staying equally satisfied.
It equals the slope of the indifference curve and diminishes as you move along it, the more you have of a good, the less of the other you'll sacrifice for it. At the optimal bundle, the MRS equals the ratio of the goods' prices.
Marginal Rate of Substitution: a worked example
A student is choosing between coffees and bagels. At her current bundle the marginal utility of one more coffee is 24 utils and the marginal utility of one more bagel is 8 utils, so the marginal rate of substitution of coffee for bagels is 24 divided by 8, which is 3 bagels per coffee. Coffee costs $3 and a bagel costs $1.50, so the price ratio is 3 divided by 1.50, or 2. Because 3 exceeds 2, she values a coffee more than the market charges for one, so she should buy more coffee and fewer bagels. As she does, the marginal utility of coffee falls to 18 and the marginal utility of bagels rises to 9. The rate is now 18 divided by 9, or 2, matching the price ratio. Check it with the equal marginal rule: 18 divided by 3 is 6 utils per dollar, and 9 divided by 1.50 is also 6.
The mistake students make with marginal rate of substitution
Students flip the ratio. The rate of substitution of good X for good Y equals the marginal utility of X divided by the marginal utility of Y, and at the optimum it equals the price of X divided by the price of Y. Writing marginal utility of Y over marginal utility of X while keeping the price ratio in X over Y order sets up the wrong condition and points at the wrong bundle. The fix is to keep whichever good sits on the horizontal axis in the numerator on both sides. A second slip is reporting the rate as negative because the curve slopes down, when it should be stated as a positive magnitude.
Marginal Rate of Substitution questions
How do you calculate the marginal rate of substitution?
MRS at a point equals the absolute value of the slope of the indifference curve there. From a table of equally preferred bundles, compute it as the change in the vertical good divided by the change in the horizontal good, then drop the minus sign. From marginal utilities, it equals the marginal utility of the good being gained divided by the marginal utility of the good being given up. All three routes give the same number at the same bundle.
Why does the marginal rate of substitution diminish?
Diminishing marginal utility drives it. As a consumer piles up more of one good, each extra unit of that good adds less satisfaction, while the good being given up grows scarcer so each remaining unit matters more. Willingness to trade the second good away for the first therefore falls as you move down and to the right along an indifference curve, which is exactly what makes the curve bow toward the origin.
What is the difference between the marginal rate of substitution and the price ratio?
MRS describes preferences, the rate at which a consumer is willing to trade one good for another with no change in satisfaction. The price ratio describes the market, the rate at which the consumer is able to trade, set by the two prices. Consumer choice theory brings them together: when willingness exceeds ability, the consumer buys more of the first good, and the optimal bundle sits where the two rates are equal.
Related terms
Common comparisons
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated